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Coupled Systems Mechanics Volume 4, Number 1, March 2015 , pages 1-18 DOI: https://doi.org/10.12989/csm.2015.4.1.001 |
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Localized particle boundary condition enforcements for the state-based peridynamics |
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C.T. Wuand Bo Ren
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| Abstract | ||
| The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach. | ||
| Key Words | ||
| state-based; peridynamics; convex kernel approximation; boundary condition | ||
| Address | ||
| C.T. Wu: Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA Bo Ren: Department of Civil and Environmental Engineering, University of California, Berkeley CA 94720, USA | ||
